The degree to which control can be exercised over assembly of micro-objects, objects whose dimensions measure in microns, can make a significant difference in a number of technologies. For example, manufacturing of reconfigurable electrical circuits can be improved by being able to accurately control positioning of micro-objects such as capacitors and resistors to manufacture a circuit with a desired behavior. Similarly, production of photovoltaic solar cell arrays can benefit from being able to put photovoltaic cells with certain qualities into particular positions on the arrays. Such cells can be too small to allow for a desired placement of the cells via human or robotic manipulation, and another kind of transportation mechanism is needed. Micro-assembly of particles can also be used to engineer the microstructure of materials. Biological cells being assembled into tissue need to be positioned and oriented. Achieving rapid directed assembly of micro objects to desired positions and with desired orientations is generally needed. Many other technological fields exist where increasing control over assembly of micro-objects can provide significant benefits.
Existing methods do not allow for control of movement of micro-objects with the required degree of precision. For example, uncontrolled mechanical agitation is typically used for directed particle assembly. However, this technique fails to achieve the near 100% yield necessary for certain industrial applications, such as electronics assembly.
Previous work has also attempted to use an electric field to direct movement of micro-objects. For example, Edwards et al., “Controlling Colloid Particles With An Electric Field,” discusses control of colloid particle ensembles (1 μm to 3 μm in diameter) and individual colloids using inhomogeneous electric fields. In particular, the individual colloid particles and the ensembles of the colloid particles suspended in water and sodium hydroxide solutions are manipulated through electrophoresis and electroosmosis using two parallel electrodes. The manipulation is done with the assumption that the electric field is completely dictated by the two parallel electrodes and is not disturbed by presence of the particles. Optical-based feedback control is used to monitor assembly and disassembly of colloid crystals. The feedback control focuses on groups of particles, thus not being able to put a particular particle in a desired position. However, the relative size of the colloids to the electrodes employed to generate the field, the medium in which the particles were immersed, and the resulting mathematical models, do not allow the described techniques to be used in certain industrial applications. In particular, the described techniques are not suitable for assembling micro-objects even slightly larger than those discussed in the Edwards paper. Further, the control schemes used involve high frequency signals (MHz), which further limits the applicability of such techniques.
Other works, such as Xue et al., “Optimal design of a colloidal self-assembly process.” IEEE Transactions on Control Systems Technology, 22(5):1956-1963, September 2014, and Xue et al., “Mdp based optimal control for a colloidal self-assembly system” American Control Conference (ACC), 2013, pages 3397-3402, June 2013, discuss using a Markov-Decision Process optimal control policy to control a stochastic colloidal assembly and drive the system to a desired high-crystallinity state. Actuator-parametrized Langevin equations are used to describe the system dynamics. However, the described approach does not allow direct manipulation of individual particles. As individual particle control is even more difficult when assembling electrical circuits, whether the described techniques can be used for electrical circuit assembly remains unclear. In addition, the particle size (≈3 μm in diameter) described in these works poses little disturbance to the electric field that is completely shaped by an actuation potentials. Moreover, the time scale for achieving the desired state would make the goal of high throughput challenging to achieve when the described techniques are applied.
Still other works, such as Qian et al., “On-demand and location selective particle assembly via electrophoretic deposition for fabricating structures with particle-to-particle precision,” Langmuir, 31(12):3563-3568, 2015, PMID: 25314133, have demonstrated single particle precision and location selective particle deposition, with electrophoretic forces being the primary drive for particle (2 μm polystyrene beads) manipulation. Shaping the energy landscape by building large energy wells closed to the desired location of the nano-particles was the chosen approach for controlling the formation of nano-structures. Although an important part in fabricating structures, the described techniques have limited industrial applications as particle deposition would not suffice for achieving potentially complex structures that may appear in electrical circuits. In addition this approach is not compatible with a subsequent transfer of the assembly to a final substrate, which is generally needed for the assembly to be used in most applications.
Still other techniques for control of assembly of microscopic particles have been proposed. For example, R. Probst et al. “Flow control of small objects on chip: Manipulating live cells, quantum dots, and nanowires,” IEEE Control Systems, 32(2):26-53, April 2012, describes using electric field induced electroosmotic flow actuation to precisely manipulate cells, quantum dots and nano-wires. Linear models in the electrode potentials for the particle motion are obtained and are used to design control schemes using least square methods. In addition, the particles' effect on the electric field distribution is negligible. Thus, this model is inapplicable where the linearity no longer holds and electrode potentials are where the electric field is affected by the particle position. Another approach is described in U.S. Pat. Nos. 7,651,598 and 8,110,083, issued to Shapiro et al. focuses on fluid flow actuation to control fluid flow fields to move particles. The main mechanism for particle transport described by Shapiro et al. is electroosmoisis. This mechanism results in a linear control scheme in the voltages applied to the electrodes. In addition, the Shapiro approach for generating control commands involves inverting a matrix, an operation which does not scale with the size of electrodes and may not be practical when a large number of electrodes is involved.
Still other techniques have been proposed. For example, since both electrophoretic forces as well as fluid motions of electro-osmotic flows can be used to drive particles, water based solution in which particles are immersed is a popular choice that have been explored in works such as Tolley et al., “Dynamically programmable fluidic assembly.” Applied Physics Letters, 93(25), 2008. However, these models are applicable to particles that are spherical, and may not be suitable for controlling particles of other shapes and thus have limited industrial applicability.
Accordingly, there is a need for a way to control movement of micro-objects with a degree of precision and scalability sufficient for industrial applications.